Can I pray (Sunnah)of the Fajr after the Fajr?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

If you find a congregation performing the obligatory Fajr prayer and you have not yet performed the Sunnah of Fajr, then you have to join them and later perform the Sunnah of Fajr. The evidence for this is the Hadeeth of Qays ibn Fahd who said: “The Prophet saw me performing two Rak'ahs after finishing the Fajr prayer. He asked: “What are these two Rak'ahs?' "What is this prayer?" I said: “O Messenger of Allah! I did not perform the two Rak'ahs that precede the prayer of Fajr, so I performed them now.” [Ahmad, Abu Dawood and at-Tirmithi]

The Prophet did not make any comment. So, the silence of the Prophet proves that it is permitted. However, it is likeable to perform these two Sunnah Rak'ahs if one misses performing them before Fajr after the sunrise. The Prophet said: “Whoever missed performing the two Rak'ahs of Fajr, he should perform them after sunrise.” [At-Tirmithi]

Allah knows best.